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Question #42110

Difficulty: 8/10 | 🟢 Free

The Question

A spherical liquid drop of radius $R$ and surface tension $T$ is placed in a vacuum. It is given a total charge $Q$ which is uniformly distributed over its surface. If the outward electrostatic pressure exactly balances the inward pressure due to surface tension, what is the magnitude of the charge $Q$ ? (Assume $\epsilon_0$ is the permittivity of free space)

Options

A.
$8\pi \sqrt{\epsilon_0 T R^3}$
B.
$8\pi \sqrt{2\epsilon_0 T R^3}$
C.
$4\pi \sqrt{2\epsilon_0 T R^3}$
D.
$4\pi \sqrt{\epsilon_0 T R^3}$

Check Your Answer

Correct Answer

Step-by-Step Solution

Explanation

How the Examiner Thinks

Multi-Concept_Bridge

Master problems that require linking physics and math concepts to solve complex competitive questions.

Concepts Behind This Question

Excess Pressure|Self-Energy of Charged Sphere|Integration

Why This Question Is Tricky

Common Mistakes

This question tests the student's ability to correctly identify and balance boundary pressures in a charged fluid system.

A common trap is confusing a liquid drop (one surface, $P = 2T/R$ ) with a soap bubble (two surfaces, $P = 4T/R$ ), which leads to an incorrect factor of $\sqrt{2}$ .

Another frequent mistake is incorrectly calculating the electrostatic pressure as $\sigma^2/\epsilon_0$ instead of $\sigma^2/2\epsilon_0$ , which stems from failing to average the electric field across the surface charge layer.

Equating the correct local boundary forces is essential for understanding the Rayleigh limit of charged drops.

Quick Facts About This Question

Question Information

Subject	Physics
Chapter	Mechanical Properties of Fluids - Class 11 Part 2
Concept	Excess Pressure (Laplace Law)
Difficulty	8
Cognitive Load	7
Target Solve Time	160 sec
Access	Free